\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\usepgfplotslibrary{groupplots}
\usepgfplotslibrary{fillbetween}

\usepackage{filecontents}

\begin{filecontents}{testdata.dat}
t lineLow lineHigh lineMedian
0 1 1 1
1 2 2 2
2 2 3 2.5
3 2 4 3
4 2 4 3
\end{filecontents}

\begin{document}

\begin{tikzpicture}
    \begin{groupplot}
    [
        group style={group size=1 by 2, vertical sep=30pt},
    ]
        \nextgroupplot
        [
        ]

        \addplot[name path=lineLow] table[x=t, y=lineLow] {testdata.dat};
        \addplot[name path=lineHigh] table[x=t, y=lineHigh] {testdata.dat};
        \addplot[fill=red] fill between[of=lineLow and lineHigh];
    \end{groupplot}
\end{tikzpicture}

\end{document}
